, £/O(l/:A II-d- c(--1S" NASA Contractor Report 198426 Probabilistic Material Strength Degradation Model for Inconel 718 Components Subjected to High Temperature, High-Cycle and Low-Cycle Mechanical Fatigue, Creep and Thermal Fatigue Effects Callie C. Bast and Lola Boyce The University o/Texas at San Antonio San Antonio, Texas November 1995 Prepared for Lewis Research Center UnderGrant NAG3-867 • .•. '-, .. .. National Aeronautics and Space Administration https://ntrs.nasa.gov/search.jsp?R=19960008692 2018-06-20T07:41:39+00:00Z
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,
£/O(l/:A II-d- c(--1S"
NASA Contractor Report 198426
Probabilistic Material Strength Degradation Model for Inconel 718 Components Subjected to High Temperature, High-Cycle and Low-Cycle Mechanical Fatigue, Creep and Thermal Fatigue Effects
Callie C. Bast and Lola Boyce The University o/Texas at San Antonio San Antonio, Texas
November 1995
Prepared for Lewis Research Center UnderGrant NAG3-867
Trade names or manufacturers' names are used in this report for identification only. This usage does not constitute an official endorsement, either expressed or implied, by the National Aeronautics and Space AdminiStration.
•
•
PROBABILISTIC MATERIAL STRENGTH DEGRADATION MODEL FOR
INCONEL 718 COMPONENTS SUBJECTED TO HIGH TEMPERATURE, HIGH· CYCLE AND LOW-CYCLE MECHANICAL FATIGUE, CREEP AND
THERMAL FATIGUE EFFECTS
Prepared by:
Callie C. Bast, M.S.M.E., Research Engineer Lola Boyce, Ph. D., P. E., Principal Investigator
Final Technical Report of Project Entitled
Development of Advanced Methodologies for Probabilistic Constitutive Relationships
of Material Strength Models, Phases 5 and 6
NASA Grant No. NAG 3-867, .Supp. 5 and 6
Report Period: June 1992 to January 1995
Prepared for:
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Lewis Research Center Cleveland, Ohio 44135
The Division of Engineering The University of Texas at San Antonio
San Antonio, TX 78249 January, 1995
ABSTRACT
The development of methodology for a probabilistic material strength degradation is de
scribed. The probabilistic model, in the form of a postulated randomized multifactor equation,
provides for quantification of uncertainty in the lifetime material strength of aerospace propul
sion system components subjected to a number of diverse random effects. This model is embod
ied in the computer program entitled PROMISS, which can include up to eighteen different
effects. Presently, the model includes five effects that typically reduce lifetime strength: high
temperature, high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and thermal
fatigue. Results, in the form of cumulative distribution functions, illustrated the sensitivity of
lifetime strength to any current value of an effect. In addition, verification studies comparing
predictions of high-cycle mechanical fatigue and high temperature effects with experiments are
presented. Results from this limited verification study strongly supported that material degrada
tion can be represented by randomized multifactor interaction models.
i
NOMENCLATURE
A i current value of the ith effect
AiU ultimate value of the ith effect
AiO reference value of the ith effect
ai ith value of the empirical material constant
b fatigue strength exponent
c fatigue ductility exponent
E modulus of elasticity
K' cyclic strength coefficient
n number of effect product terms in the model
n' cyclic strain hardening exponent
N current value of high-cycle mechanical· fatigue cycles
N current value of thermal fatigue cycles
N" current value of low-cycle mechanical fatigue cycles
N p number of high-cycle mechanical fatigue cycles to failure
Np number of thermal fatigue cycles to failure
2Np number of thermal fatigue reversals to failure
N"p number of low-cycle mechanical fatigue cycles to failure
Nu ultimate value of high-cycle mechanical fatigue cycles
Nu ultimate value of thermal fatigue cycles
N"u ultimate value of low-cycle mechanical fatigue cycles
No reference value of high-cycle mechanical fatigue cycles
No reference value of thermal fatigue cycles
N"o reference value of low-cycle mechanical fatigue cycles
q material constant for temperature
r material constant for low-cycle mechanical fatigue cycles
R 2 coefficient of determination
s material constant for high-cycle mechanical fatigue cycles
S ClUTent value of material strength
So reference value of material strength
T current value of temperature
Tu ultimate value of temperature
To reference value of temperature
ii
NOMENCLATURE (continued)
t current value of creep time tF number of creep hours to failure
tu ultimate value of creep time
to reference value of creep time
u material constant for thermal fatigue cycles
v material constant for creep time lleJ2 elastic strain amplitude
1 Schematic of Data lllustrating the Effect of One Variable 'on Strength ................................•...... -:.............................................................. 4
2 Effect of Temperature (OF) on Yield Strength for Inconel718 ••••....•..••.••.•••••• 18
3 Effect of Temperature (Of')on Yield Strength for Inconel 718. (l.og-wg Plot with Linear Regression)........................................................... 19
4 Effect of High-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718. ....•.......•..•..........•.......•.......•........••••.•......... ..•..•..•••••••..•...•....•• 20
5 Effect of High-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718. (Non-sensitized Model Form) ..••.•....••••••••.•••.•..•..•.•.•••••.•..•.••. 21
6 Effect of High-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718. (Sensitized Model Form) ............•.....••......•....•...•..•••.............. 21
8 Effect ofww-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718. (Non-sensitized Model Form)............................................... 23
9 Effect ofww-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718. (Sensitized Model Form) .............••••...•...••.•.••..••..•...•.......•.•... 23
10 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718. (Linear Plot) .• .......••.•.. ............ ... .••...•••... ..... .•.•. ... ... ..•....•.. ...•.. 24
11 Effect of Creep Time (Hours) on Rupture Strength for Inconel718. (Non-sensitized Model Form) .............................................. 25
12 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718. (Sensitized Model Form) ..................................................... 25
13 Strain-life Curve for Inconel 718. .......................................••.••......•......•••••..•.. 27
14 Cyclic Stress Strain Curve for Inconel 718. ................................................... 27
15 Regression of Equation (11) Data Yielding Fatigue Ductility Coefficient, elF, and Fatigue Ductility Exponent, c. ........................................................... 28
16 Regression of Equation (12) Data Yielding Cyclic Strength Coefficient, KI, and Cyclic Strain Hardening Exponent, nl. ............................ 29
vi
LIST OF FIGURES (continued)
FIGURE PAGE
17 Regression of Equation (13) Yielding Fatigue Strength Coefficient, a'F, and Fatigue Strength Exponent, b. ....................................... 30
18 Effect of Thermal Fatigue (Cycles) on Thermal Fatigue Strength (i.e., Stress Amplitude at Failure) for Inconel 718 .......................................... 31
19 Effect of Thermal Fatigue (Cycles) on Thermal Fatigue Strength for Inconel718. (Non-sensitized Model Form) .............................................. 32
20 Effect of Thennal Fatigue (Cycles) on Thermal Fatigue Strength for Inconel 718. (Sensitized Model Form) ...................................................... 32
21 Effect of High-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Incone1718. (Sensitized Model Form Using Improved Estimates) ........•...... 36
22 Effect of Low-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel718. (Sensitized Model Form Using Improved Estimates) ...•••..••.••.• 36
23 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718. (Sensitized Model Form Using Improved Estimates) .................................... 37
24 Effect of Thermal Fatigue (Cycles) on Thermal Fatigue Strength. (Sensitized Model Form Using Improved Estimates) .................................... 37
25 Linear Regression of Temperature Data. ......................................................... 40
26 Postulated Maximum and Minimum Slopes .................................................. 41
27 Postulated Maximum and Minimum Y-intercepts ......................................... 41
28 Probability Density Function of a Normal Distribution. ................................. 42
29 Postulated Envelope of Actual and Simulated Temperature (Of) Data. .........• 43
30 Inconel 718 Model Parameters for High-Cycle Mechanical Fatigue, Cre,ep and Thermal Fatigue Effects. ............................................................... 45
31 Comparison of Various Levels of Uncertainty of High-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel718 for 2000 Thermal Fatigue Cycles and 1000 Hours of Creep at 1000 OF. .................................... 48
vii
LIST OF FIGURES (continued)
FIGURE
32 Comparison of Various Levels of Uncertainty of Creep Time (Hours) on Probable Strength for Inconel718 for lxl()6 High-Cycle Mechanical
PAGE
Fatigue Cycles and 2000 Thermal Fatigue Cycles at 1000 OF. ....................... 48
33 Comparison of Various Levels of Uncertainty of Thermal Fatigue (Cycles) on Probable Strength for Inconel 718 for Ixl06 High-Cycle Mechanical Fatigue Cycles and 1000 Hours of Creep at 1000 OF. .................................... 49
34 Comparison of Various Levels of Uncertainty of High-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel 718 for 1000 Low-Cycle Mechanical Fatigue Cycles, 2000 Thermal Fatigue Cycles and 1000 Hours of Creep at 1000 OF. ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• S2
35 Comparison of Various Levels of Uncertainty of Low-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel 718 for lxl06 High-Cycle Mechanical Fatigue Cycles, 2000 Thermal Fatigue Cycles and 1000 Hours of Creep at 1000 OF ........................................................ ~................................ 52
36 ·Comparison of Various Levels of Uncertainty of Creep Time (Hours) on Probable Strength for Inconel 718 for lx106 High-Cycle Mechanical Fatigue Cycles, 1000 Low-Cycle Mechanical Fatigue Cycles and 2000 Thermal Fatigue Cycles at 1000 °P. •••••••••....••.••••••••••.•••••••.•••..•••••••••.••.••.••••••• S3
37 Comparison of Various Levels of Uncertainty of Thermal Fatigue (Cycles) on Probable Strength for Inconel 718 for lxl06 High-Cycle Mechanical Fatigue Cycles, 1000 Low-Cycle Mechanical Fatigue Cycles and 1000 Hours of Creep at 1000 °P. .....................•..................••••••••.•••.•..................••.• S3
38 Comparison of Various Levels of Uncertainty of High-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel718. (Combination of H-C Mechanical Fatigue and High Temperature Effects by Model) ••••....•..••• 57
39 Comparison of Various Levels of Uncertainty of High-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel718. (Combination of H-C Mechanical Fatigue and High Temperature Effects by Experiment) .•.••• 57
40 Overlay of Results for a Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model and by Experiment. ................................ 58
41 Overlay of R~sults for a Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s) and by Experiment. ............................•........................................................... 60
viii
LIST OF FIGURES (continued)
BGURE PAGE
42 Overlay of Results for a Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s) and .by Experiment; N=2.SxlOS Cycles. ........................................................ 60
43 Overlay of Results for a Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s) and by Experiment; N=1.0x106 Cycles. ........................................................ 61
44 Overlay of Results for a Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s) and by Experiment; N=1.75x106 Cycles. ...................................................... 61
ix
LIST OF TABLES
TABLE PAGE
1 Variables Available in the "Fixed" Model. ....................................................... 6
2 Variables Available in the "Flexible" Model. ................................................... 7
3 Non-sensitized and Sensitized Terms for High-Cycle Mechanical Fatigue Data. ................................................................................ 14
4 Non-sensitized and Sensitized Terms for Low-Cycle Mechanical Fatigue Data. ................................................................................ 14
5 Non-sensitized and Sensitized Tenns for Creep Rupture Data. ...................... 15
6 Non-sensitized and Sensitized Tenns for Thennal Fatigue Data. .............•..... 16
7 Thermal Fatigue Data for Inconel 718. ........................................................... 26
8 Fatigue Material Properties for Inconel 718. ................................................... 30
9 Initial Estimates for the Ultimate and Reference Values. ................................ 33
10 Initial Estimates for the Empirical Material Constants .................................... 34
11 Improved Estimates for the Ultimate and Reference Values. ......................... 38
12 Improved Estimates for the Empirical Material Constants. ............................ 38
13 '93 Sensitivity Study Input to PROMISS93 for Inconel718; Temperature=l000 OP and N=2.5xlOS Cycles. .............................................. 46
14 '93 Sensitivity Study Input to PROMISS93 for Inconel 718; Temperature=I000°F and N=1.0xl06 Cycles. ............................................... 46
15 '93 Sensitivity Study Input to PROMISS93 for Inconel 718; Temperature=I000°F and N=I.75xl06 Cycles. ............................................. 47
16 Selected Cmrent Values for '93 Sensitivity Study of the Probabilistic Material Strength Degradation Model for Inconel718. .................................. 47
17 Selected Cmrent Values for '94 Sensitivity Study of the Probabilistic Material Strength Degradation Model for Inconel 718. .................................. 51
18 Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=2.5xlOS Cycles. .................................................. 55
x
LIST OF TABLES (continued)
TABLE PAGE
19 Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=l.Ox106 Cycles. .................................................. 55
20 Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=1.75x106 Cycles. ................................................ 55
21 Verification Study Input to PROMISS93 for Inconel 718; Combination by Experiment, N=2.5x1OS Cycles ........................................... 56
22 Verification Study Input to PROMISS93 for Inconel 718; Combination by Experiment, N=1.Ox106 Cycles ........................................... 56
23 Verification Study Input to PROMISS93 for Inconel 718; Combination by Experiment, N=1.75x106 Cycles ......................................... 56
24 Modified Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=2.5x1OS Cyc~es. .................................................. 59
25 Modified Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=l.Ox106 Cycles. .................................................. 59
26 Modified Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=1.75x106 Cycles. ................................................ 59
A.1 Inconel 718 High Temperature Tensile Data. ................................................. 68
for ultimate and reference values are determined using available data for Inconel 718. A
transformation to improve model sensitivity is then discussed. Section 5 presents
experimental material data for Inconel 718 and displays the data in the form utilized by the
multifactor equation embodied in PROMISS. Temperature, high-cycle mechanical fatigue,
low-cycle mechanical fatigue, creep and thermal fatigue data for Inconel 718 are presented.
Linear regression of the data is performed to provide first estimates of the empirical material
constants, aio used to calibrate the model. Additional calibration techniques to improve model
1
accuracy are then discussed. In Section 6, methodology for estimating standard deviations of
the empirical material constants is developed as a means for dealing with limited data. These estimated values for the standard deviation, rather than expert opinion, may be used with
greater confidence in the probabilistic material strength degradation model. Section 7 presents
and discusses cases for analysis that resulted from two sensitivity studies. '93 Sensitivity
Study examined the combined effects of high-cycle mechanical fatigue, creep and thermal
fatigue at elevated temperatures, while '94 Sensitivity Study included four effects - low-cycle
mechanical fatigue along with the three previous effects. Results, in the form of cumulative
distribution functions, illustrate the sensitivity of lifetime strength to any current value of an
effect. Section 8 presents and discusses model verification studies that were conducted to
evaluate the ability of the multifactor equation to model two or more effects simultaneously.
Available data allowed for verification studies comparing a combination of high-cycle
mechanical fatigue and temperature effects by model to the combination of these two effects by
experiment. Methodology and results are reiterated and discussed in Section 9. Conclusions
of the current research and recommendations for future research conclude this report. The raw
data for all effects, along with material and heat treatment specifications, are provided in the
appendix.
2
2.0 THEORETICAL BACKGROUND
Previously, a general material behavior degradation model for composite materials,
subjected to a number of diverse effects or variables, was postulated to predict mechanical and
thermal material properties [8,9,13,14]. The resulting multifactor equation summarizes a
proposed composite micromechanics theory and has been used to predict material properties
for a unidirectional fiber-reinforced lamina based on the corresponding properties of the
constituent materials.
More recently, the equation has been modified to predict the lifetime strength of a
single constituent material due to "n" diverse effects or variables [4,5,6]. These effects could
include variables such as high temperature, creep, high-cycle mechanical fatigue, thermal
fatigue, corrosion or even radiation attack. For these variables, strength decreases with an
increase in the variable [12]. The general form of the postulated equation is
n [ ]ai S II A·u-A. , _ 1 1
So - i=l AiU - AiO (1)
where Ah AiU and AiO are the current, ultimate and reference values, respectively, of a
particular effect; ai is the value of an empirical material constant for the ith product terms of
variables in the model; S and So are the current and reference values of material strength. Each
tenn has the property that if the current value equals the ultimate value, the lifetime strength
will be zero. Also, if the current value equals the reference value, the term equals one and
strength is not affected by that variable. The product form of equation (1) assumes·
independence between the individual effects. This equation may be viewed as a solution to a
separable partial differential equation in the variables with the further limitation or
approximation that a single set of separation constants, ait can adequately model the material
properties.
Calibration of the model is achieved by appropriate curve-fitted least squares linear
regression of experimental data [19] plotted in the form of equation (1). For example, data for
just one effect could be plotted on log-log paper. A good fit for the data may be obtained by
linear regression as shown schematically in Figure 1. Dropping the subscript "i" for a single
variable, the postulated equation is obtained by noting the linear relation between log S and
3
log [(Au - Ao)/(Au - A)], as follows:
logS=-a IOg[AU-AO]+IOgSO Au- A
IOg~=-alOg[AU -AO] So Au- A
~=[AU-Aora So Au-A
or,
S Au-A [ ]
a
So = Au-Ao .
log S
log$o
(2a)
(2b)
-a = slope
Fig. 1 Schematic of Data illustrating the Effect of One Variable on Strength.
4
..
This general material strength degradation model, given by equation (1), may be used to estimate the lifetime strength, SISo, of an aerospace propulsion system component operating
under the influence of a number of diverse effects or variables. The probabilistic treatment of
this model includes "randomizing" the deterministic multifactor equation through probabilistic
analysis by simulation and the generation of probability density function (p.d.f.) estimates for lifetime strength, using the non-parametric method of maximum penalized likelihood [20,22].
Integration of the probability density function yields the cumulative distribution function (c.d.f.) from which probability statements regarding lifetime strength may be made. This probabilistic material strength degradation model, therefore, predicts the random lifetime strength of an aerospace propulsion component subjected to a number of diverse random
effects.
The general probabilistic material strength degradation model, given by equation (1),
is embodied in the FORTRAN program, PROMISS (f,mbabilistic M.aterial £trength
S.imulator) [6]. PROMISS calculates the random lifetime strength of an aerospace propulsion component subjected to as many as eighteen diverse random effects. Results are presented in the form of cumulative distribution functions of lifetime strength, S/So-
5
3.0 PROMISS COMPUTER PROGRAM
PROMISS includes a relatively simple "fIxed" model as well as a "flexible" model.
The fIxed model postulates a probabilistic multifactor equation that considers the variables
given in Table 1. The general form of this equation is given by equation (1), wherein there are
now n = 7 product terms, one for each effect listed below. Note that since this model has
seven terms, each containing four parameters of the effect (A, Au, Ao and a), there are a total
of twenty-eight variables. The flexible model postulates the probabilistic multifactor equation
that considers up to as many as n = 18 effects or variables. These variables may be selected to
utilize the theory and experimental data currently available for the particular strength
degradation mechanisms of interest. The specifIc effects included in the flexible model are
listed in Table 2. To allow for future expansion and customization of the flexible model, six
"other" effects have been provided.
Table 1. Variables Available in the ''Fixed'' Model.
ith Primitive Primitive Variable Variable Type
1 Stress due to static load
2 Temperature
3 Chemical reaction
4 Stress due to impact
5 Mechanical fatigue
6 Thennal fatigue
7 Creep
6
Table 2 Variables Available in the "Flexible" Model.
A. Environmental Effects
1. Mechanical
a. Stress b. Impact c. Other Mechanical Effect
2. Thermal
.a. Temperature Variation. b. Thermal Shock c. Other Thermal Effect
3. Other Environmental Effects
a. Chemical Reaction b. Radiation Attack c. Other Environmental Effect
B. Time-Dependent Effects
1. Mechanical a. Creep . b. Mechanical Fatigue c. Other Mech. Time-Dependent Effect
2. Thermal
a. Thermal Aging b. Thermal Fatigue c. Other Thermal Time-Dependent Effect
3. Other Time-Dependent Effects
a. Corrosion b. Seasonal Attack c. Other Time-Dependent Effect
The considerable scatter of experimental data and the lack of an exact description of
the underlying physical processes for the combined mechanisms of fatigue, creep, temperature
variations, and so on, make it natural, if not necessary to consider probabilistic models for a
strength degradation modeL Therefore, the fixed and flexible models corresponding to
equation (1) are "randomized", and yield the random lifetime material strength due to a number
7
of diverse random effects. Note that for the fIXed model~ equation (1) has the following form:
where Ai. AiU and AiO are the current, ultimate and reference values of the ith of seven effects
as given in Table 1, and ai is the ith empirical material constant. In general, this expression can be written as,
8/80 = f(XV, i = 1, ... , 28 (4)
where Xi represents the twenty-eight variables in equation (3). Thus, the fixed model is
"randomized" and assumes all the variables, Xit i = 1, ... , 28, to be random. For the flexible
model~ equation (1) has a form analogous to equations (3) and (4)~ except that there are as
many as seventy-two random variables. Applying probabilistic analysis [22] to either of these
randomized equations yields the distribution of the dependent random variable, lifetime
material strength, 8/So.
Although a number of methods of probabilistic analysis are available, simulation was
chosen for PROMISS. Simulation utilizes a theoretical sample generated by numerical
techniques for each of the random variables [22]. One value from each sample is substituted
into the functional relationship, equation (3), and one realization of lifetime strength, S/So, is
calculated. This calculation is repeated for each value in the set of samples, yielding a
distribution of different values for lifetime strength.
A probability density function (p.d.f.) is generated from these different values of
lifetime strength, using a non-parametric method, maximum penalized likelihood. Maximum
penalized likelihood generates the p.d.f. estimate using the method of maximum likelihood
together with a penalty function to smooth it [20]. Integration of the generated p.d.f. results in
the cumulative distribution function (c.d.f.), from which probabilities of lifetime strength can
be directly noted.
In summary, PROMISS randomizes the following equation:
n [ ]ai S IT A·u-A· _ 1 1
So - i=l AiU - AiO
(1)
There is a maximum of eighteen possible effects that may be included in the model. For the
flexible model option, they may be chosen by the user from those in Table 2. For the flXed
model option, the variables of Table 1 are used. Within the product term for each effect, the
current, ultimate and reference values, as well as the empirical material constant, may be
modeled as either detenninistic, normal, lognormal, or Wiebull random variables. Simulation
8
is used to generate a set of realizations for lifetime random strength, S/So, from a set of
realizations for the random variables of each product term. Maximum penalized likelihood is
used to generate the p.d.f. estimate of lifetime strength, from the set of realizations of lifetime
strength. Integration of the p.d.f. yields the c.d.f., from which probabilities of lifetime strength
can be ascertained. PROMISS also provides information on lifetime strength statistics, such
as the mean, variance, standard deviation and coefficient of variation.
9
4.0 STRENGTH DEGRADATION MODEL FOR INCONEL 718
The probabilistic material strength degradation model, in the form of the multifactor
equation given by equation (1), when modified for a single effect, results in equation (5)
below.
S Au-A Au-Ao [ ]a [ ]-a So = Au-Ao = Au- A
(5)
Appropriate values for the ultimate, Au, and reference quantities, Ao, had to be estimated as
part of the initial calibration of the multifactor equation for Inconel 718. Based on actual
Inconel718 data, these values were selected accordingly for each effect
4.1 Temperature Model
Equation (5), when modified for the effect of high temperature only, becomes:
~=[TU-TO]-q , So Tu- T
(6a)
where Tu is the ultimate or melting temperature of the material, To is a reference or room
temperature, T is the current temperature of the material, and q is an empirical material constant
that represents the slope of a straight line fit of the modeled'data on log-log paper. A logical
choice for the ultimate temperature value is the average melting temperature (2369 oF) of
Inconel718. Therefore, this value was an initial estimate for the ultimate temperature value,
Tu. An estimate of 75°F or room temperature was used for the reference temperature value,
To. Substitution of these values into equation (6a) above results in equation (6b) below. Thus,
equation (6b) models the effect of high temperature on the lifetime strength of the specified
material,InconeI718.
~=[TU -To]-q = [2369-75J-q So Tu -T 2369-T
(6b)
10
4.2 High-Cycle Mechanical Fatigue Model
Equation (5), when modified for the effect of high-cycle mechanical fatigue,
becomes:
(7a)
where Nu is the ultimate number of cycles for which fatigue strength is very small, No is a
reference number of cycles for which fatigue strength is very large, N is the current number of
cycles the material has undergone, and s is the empirical material constant for the high-cycle
mechanical fatigue effect. An initial estimate of lxl010 was used for the ultimate number of
cycles, Nu. since mechanical fatigue data beyond this value was not found for Inconel 718. An
initial estimate of 0.5 or half a cycle was used for the reference number of cycles, No.
Substitution of these values into equation (7 a) results in the high-cycle mechanical fatigue
model for Inconel 718, as given below by equation (7b).
~=[1010 _0.5]-S SO 10lD_N
(7b)
Since the high-cycle fatigue domain is associated with lower loads and longer lives, or high
numbers of cycles to failure (greater than 1()4 or lOS cycles), data consisting of cycle values
less than 5xl()4 fall into the low-cycle fatigue regime and therefore, may be modeled by the
low-cycle mechanical fatigue model presented in Section 4.3.
4.3 Low-Cycle Mechanical Fatigue Model
Equation (5), when modified for the effect of low-cycle mechanical fatigue, becomes:
~ _ [N"u - N"o ]-' - " " , So Nu-N
(8a)
where Nltu is the ultimate number of cycles for which fatigue strength is very low, Nlto is a
reference number of cycles for which fatigue strength is very high, Nit is the current number of
cycles the material has undergone, and r is the empirical material constant for the low-cycle
mechanical fatigue effect. An initial estimate of lxlOS was used for the ultimate number of
cycles, N"u. since niechanical fatigue cycle values beyond this value fall into the high-cycle
fatigue domain. An initial estimate of 0.5 or half a cycle was used for the reference number of
cycles, Nita. Substitution of these values into equation (8a) results in the low-cycle mechanical
11
fatigue model for Inconel 718, as given below by equation (8b).
l. = [1 x lOS - o.~]-r So lx10s-N
4.4 Creep Model
Equation (5), when modified for the effect of creep, becomes:
~=[tu -toJ-v , So tu-t
(8b)
(9a)
where tu is the ultimate number of creep hours for which rupture strength is very small, to is a
reference number of creep hours for which rupture strength is very large, t is the current
number of creep hours, and v is the empirical material constant for the effect of creep. An
initial estimate of 1xl()6 was used for the ultimate number of creep hours, tu, due to the fact
that creep rupture life data beyond this value was not found for Inconel 718. An initial estimate
of 0.25 hours or fifteen minutes was used for the reference number of creep hours, to. Substitution of these values into equation (9a) results in equation (9b) below.
~ = [106 ~ 0.25]-V (9b)
So 10 -t
4.5 Thermal Fatigue Model
The fifth and final effect for which Inconel718 data was obtained is thermal fatigue.
Thermal fatigue has been extensively discussed in the literature [10, 17, 24]. When modified
for the effect of thermal fatigue, equation (5) becomes:
(lOa)
where Nu is the ultimate number of thermal cycles for which thermal fatigue strength is very
small, N'o is a reference number of thermal cycles for which thermal fatigue strength is very
large, N' is the current number of thermal cycles the material has undergone, and u is an
empirical material constant that represents the slope of a straight line fit of the modeled· data on
log-log paper.
Thermal fatigue is in the regime of low-cycle fatigue (less than 1()4 or lOS cycles),
therefore, an intennediate value of 5xl04 cycles was an initial estimate for the ultimate number
12
of thermal fatigue cycles, N'u. An initial estinuLte of 0.5 or half a cycle was used for the
reference number of cycles, N' o. Substitution of these values into equation (lOa) results in the
thermal fatigue model for Inconel7l8, as given by equation (lOb) below.
~=[5XI0:-0·?ru. So 5xlO-N
(lOb)
4.6 Model Transformation
In the case of high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and
thermal fatigue, the current value and the reference value are small compared to the ultimate
value. Therefore, regardless of the current value used, the term [ Au - A ] remains Au-Ao
approximately constant. In order to sensitize the model for these four effects, the 10glO of each
value was used. As seen in Tables 3 through 6, this transformation significantly increases the
sensitivity of a product term to the data used within it. In addition, this transformation results
in better statistical linear regression fits of the data, as seen later in Figures 6, 9, 12 and 20 of
Section 5. Hence, the general term [ Au -A ] was modified to the sensitized form, Au-Ao
[ 10g(Au) -log(A) ], for these four effects. The program, PROMISS94, modifies the
log(Au) -log(Ao)
program, PROMISS, to allow for the sensitized fonn of these four effects.
13
Table 3 Non-sensitized and Sensitized Terms for High-Cycle Mechanical Fatigue Data.
Test Temperature, Cycles, [ (1OIO)_(N) ] [ Jog(IOIO)_log(N) ] of N (1010)_ (0.5) log(1010
Fig. 6 Effect of High-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel 718. (Sensitized Model Form.)
21
5.5 Low-Cycle Mechanical Fatigue Data
The general model for the low-cycle mechanical fatigue effect uses stress-life (a-N)
data obtained from experimental strain-life (e-N) data. The low-cycle mechanical fatigue data
presented in Table 4 resulted from closed-loop strain controlled tests performed in air with
induction heating [7]. These tests were conducted at a constant temperature of 1000 OF and a
strain rate of 4x10-3 sec-I.
By equation (11), the stress amplitude, Aa/2, was calculated using the elastic strain
and an average value ofE=24.5x106 psi (modulus of elasticity for Inconel718 at
1000 oF) [15].
A2a =E[a;e] (11)
The resulting low-cycle mechanical fatigue stress-life (a-N) data were plotted in various
forms, including non-sensitized and sensitized model forms. Figure 7 presents the low-cycle
mechanical fatigue data and shows the effect of mechanical fatigue cycles on stress amplitude
at failure (i.e., fatigue strength) for the given test temperature of 1000 OF. As with the high
cycle mechanical fatigue data, the fatigue strength of Inconel 718 decreases as the number of
cycles increases. Figures 8 and 9 show the data in the non-sensitized form of equation (8b)
and the sensitized model form, respectively. Linear regression of the data produced a fIrst
estimate of the empirical material constant, r, for the low-cycle mechanical fatigue effect, as
given by the slope of the linear regression fIt. As seen by the regression fit in Figures 8 and 9, the R2 (goodness of fit) value is significantly higher for the sensitized model form.
180000 -Ci) a. -:z:: 160000 t; z w a: 140000 t; w ~ 120000
~ u. 100000 -t----,..-----r---""T---...__-__r--_.
o 10000 20000 30000
N" F (CYCLES TO FAILURE)
Fig. 7 Effect of Low-Cycle Mechanical Fatigue ( Cycles) on Fatigue Strength for Inconel 718.
22
,.
-~ 5.3 -5.2
RI\2 = 0.680
5.1 • • • • 5.0
0.00 0.02 0.04 0.06 0.08 0.10
LOG [(1 0"S-0.S)/(1 O"S-N")]
Fig. 8 Effect of Low-Cycle Mechanical Fatigue (Cycles) on Fatigue Strength for Inconel718. (Non-sensitized Model Form)
Fig. 10 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718. (Linear Plot)
24
-in 11--:c ~ Z w a: ~ w a: ::)
Ii: ::) a: CJ 9
-~ -
5.3
... T=1000°F
5.1618 - 10.922x RA2 = 0.722 a T=1100 of
5.1 0 T=1200 OF
• T=1300°F
4.9
- 11.080x RA2 = 0.701
4.7 Y = 5.0021 - 50.520x RA2 = 0.843
RA2 = 0.806 4.5 0.000 0.005 0.010 0.015 0.020
LOG[(1 OA6-0.25)/(1 0 A 6-t)]
Fig. 11 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718. (Non-sensitized Model Form)
5.3
5.1
4.9
4.7
... T=1000°F a T=1100°F
o T=1200°F
RA2 = 0.994
3x RA2 = 0.992
RA2 = 0.991
• T=1300 OF RA2 = 0.998
4.5;-----~--~~--~----~----~~~~--~----~
0.0 0.2 0.4 0.6 0.8
LOG[LOG(1 OA6)-LOG(0.25»/(LOG(1 OA6)-LOG(t»]
Fig. 12 Effect of Creep Time (Hours) on Rupture Strength for Inconel 718. (Sensitized Model Form)
25
5.7 Thermal Fatigue Data
Low cycle fatigue produces cumulative material damage and ultimate failure in a
component by the cyclic application of strains that extend into the plastic range. Failure
typically occurs under 1()4 or lOS cycles. Low cycle fatigue is often produced mechanically
under isothermal conditions. However, machine components may also be subjected to low
cycle fatigue due to a cyclic thermal field. These cyclic temperature changes produce thermal
expansions and contractions that, if constrained, produce cyclic stresses and strains. These
thermally induced stresses and strains result in fatigue failure in the same manner as those
produced mechanically.
The general model for the thermal fatigue effect uses stress-life (O'-N) data obtained
from experimental strain-life (e-N) data. The thermal fatigue data presented in Table 7 resulted
from thermomechanical fatigue tests conducted on test bars annealed at 1800 OF and aged [17].
The temperature and strain were computer-controlled by the same triangular waveform with
in-phase cycling at a frequency of 0.0056 Hz.. The temperature was cycled between a
minimum temperature of 600 OF and a maximum temperature of 1200 OF, with a mean
temperature of approximately 900 OF. This total strain amplitude data and plastic strain
amplitude data were used to construct the strain-life curves presented in Figure 13.
Table 7 Thermal Fatigue Data for Inconel 718.
Cycles to Total Strain Plastic Strain Stress Failure Amplitude, Amplitude, Amplitude,
N'p &T/2 /:lEp/2 /:lcr/2 (psi)
45 0.0100 0.0050 126,500
140 0.0075 0.0029 116,380
750 0.0050 0.0011 98,670
9750 0.0040 0.0003 93,610
26
.1
III Q ::)
.01 I-::; a. :Ii CC
Z C .001 a: I-eI)
.0001 10
6-
o 6
6 o
o
100 1000
CYCLES TO FAILURE, NF
6 TOTAL STRAIN
o PLASTIC STRAIN
o
10000
Fig. 13 Strain-life Curve for Incone1718.
By equation (12), the stress amplitude, /lo/2, was calculated using total and plastic strain amplitudes, llET/2 and llEp/2, respectively, along with an average value ofE=25xl06 psi
(modulus of elasticity for Inconel 718 at 900 oF) [15].
flo = E[/lET _/lEP] 2 2 2
(12)
The resulting stress amplitude data were then plotted against the plastic strain amplitude data to
produce the cyclic stress-strain curve shown below in Figure 14.
140000
:::-f/) Do -w
120000 c ::)
t:: .... Do :Ii cc f/) 100000 f/) w a: l-f/)
~oo+---~~--~----~----~--~~--~
0.000 0.002 0.004 0.006
PLASTIC STRAIN AMPLITUDE
Fig. 14 Cyclic Stress-Strain Curve for Incone1718.
27
Using power law regression techniques [1] and the data in Table 7, fatigue properties
for Inconel 718 were calculated. These properties were calculated and compared with known
established values in order to check the validity of the data. The plastic portion of the strain-life
curve (Figure 13) may be represented by the following power law function:
6ep • ( .)C T=eF 2NF ' (13)
where 6ep/2 is the plastic strain amplitude and 2NF are the reversals to failure. A power law
regression analysis of the data yielded two fatigue properties, namely, the fatigue ductility coefficient, elF, and the fatigue ductility exponent, c. These two properties are indicated
graphically, along with their coefficient of determination, R2, in Figure 15. Regression
statistics, such as R2, were obtained to indicate whether or not a power law representation of
the relationship between plastic strain amplitude and reversals to failure was appropriate. As
commned by the high R2 value in Figure 15, the power law function of equation (11) well represents the relationship between 6ep/2 and 2NF.
Fig. 20 Effect of Thermal Fatigue (Cycles) on Thermal Fatigue Strength. (Sensitized Model Form)
32
5.8 Model Calibration
The first estimates of the ultimate and reference values for each effect are given in
Table 9. First estimates of the empirical material constants, previously determined from linear regression of high temperature. high-cycle mechanical fatigue. low-cycle mechanical fatigue. creep and thermal fatigue data, are snmmarized in Table 10. These initial estimates were used
to calibrate the strength degradation model specifically for Inconel 718. Thus. model accuracy is dependent on proper selection of ultimate and reference values. which in turn influence the
values of the empirical material constants.
Table 9 Initial Estimates for the Ultimate and Reference Values.
Ultimate Estimated Reference Estimated Effect Value Ultimate Value Value Reference Value
Symbol Symbol Temperature Tu 2369 To 75
High-Cycle Nu lxl010 No 0.5 Mechanical Fatigue
Low-Cycle N"u lxl0s N"o 0.5 Mechanical Fatigue
Creep tu lxl06 to 0.25
Thermal Fatigue Nu 5xl04 No 0.5
33
Table 10 Initial Estimates for the Empirical Material Constants.
Effect Empirical Material Estimated Value of Applicable Constant Symbol Constant Temperature (OF)
High Temperature q 0.2422 75-1300
High-Cycle s 0.3785 75 Mechanical Fatigue
High-Cycle s 0.2235 1000 Mechanical Fatigue
High-Cycle s 0.3543 1200 Mechanical Fatigue
Low-Cycle r 0.3396 1000 Mechanical Fatigue
Creep v 0.2912 1000 Creep v 0.4008 1100 Creep v 0.6243 1200 Creep v 1.1139 1300
Thermal Fatigue u 0.2368 900
As previously mentioned, the quantities used for ultimate and reference values were
initial estimates. Based on the parameters obtained from linear regression analysis of the data, i.e. slope (material constant), y-intercept (log So) and R2, an attempt to adjust these initial
estimates to improve the accuracy of the model was made. Noting that the y-intercept value
corresponds to the log of the reference strength, So, it was necessary to physically defme what
the quantity So represents. For the temperature model, given the data used, So (5.217 or
164,816 psi) estimates the yield strength of Inconel 718 at the reference temperature of 75 OF
as seen by Figure 3. In order to correlate the So for all effects to the yield strength, the ultimate
and reference values for high-cycle and low-cycle mechanical fatigue, creep and thermal fatigue
effects were adjusted. Adjusting the ultimate value influenced the slope, y-intercept and R2
values, while adjusting the reference value altered the y-intercept value but had no affect on
either the slope or R2 values. In addition, certain trends were noted. Increasing the ultimate
value increased the So value, while increasing the reference value decreased it
Based on this information, initial estimates were r~evaluated for high-cycle
mechanical fatigue, low-cycle mechanical fatigue, creep and thermal fatigue effects.
34
Reevaluation of the initial estimates for the tempe~ture effect was not necessary since this
temperature data consisted of yield strength values at various temperatures, thus So is already
correlated to a yield strength value of Inconel 718. For the high-cycle mechanical fatigue
effect, Figure 6 shows log So values of 5.1974 (157,543 psi), 5.1067 (127,850 psi) and
5.1184 (131,341 psi) for temperatures of 75, 1000 and 1200 OF, respectively. According to
average yield strength data for Inconel718 [16], these values are too low. Therefore, in order
to increase these y-intercept values, the ultimate value was varied between lxl010 and lxl011
cycles, while the reference value was varied between 0.5 and 0.25 cycles. The result was that
an ultimate value of lxl010 combined with a reference value of 0.25 yielded y-intercept values
closest to the average yield strength for corresponding temperatures. Initial ultimate and
reference values for the low-cycle mechanical fatigue, creep and thermal fatigue models were
also adjusted accordingly. Figures 21, 22, 23 and 24, show the improved ultimate and
reference values selected and display the subsequent new linear regression results of the high
These random parameters, now expressed in terms of their mean and standard deviation, were
used to define the probabilistic material strength degradation model for temperature as a
random parameter model having the following form:
S=S [TU-TO]-q =S [2369-75]-q 0. Tu -T 0 2369-T '
(16c)
where -q and So are now random variables for the slope and y-intercept, respectively • . In order to demonstrate this methodology, modifications were made to PROMISS
[6]. These modifications included providing random variable input mechanisms for So in
terms of its mean and standard deviation, adding random number generation capability for So,
and providing coding to calculate equation (16c), so that results are given in terms of strength,
S, rather than lifetime strength, S/So. The resulting values for S were calculated by simulation
using an augmented version of PROMISS called CALLIE92T. Forty values of strength, S,
corresponding to each temperature value, T, were obtained. Figure 29 displays selected
strength values of the forty calculated, along with the actual temperature data and the postulated
envelope of the random parameter model as defmed by the extreme parameter values. The
statistical frequency with which calculated values of S fell within the envelope were noted.
Since an overwhelmingly large number of S values were found to lie within the envelope, it
was ascertained that experimental temperature data beyond the known five data points would
also fall within the envelope. Thus, this estimated value of the standard deviation, rather than
expert opinion or an assumed value, can be used with greater confidence in the probabilistic
material strength degradation model embodied in PROMISS.
-~ -:c t-
~ UI a: ; Q -' UI >= CJ 9
5.25 • Actual Data • Selected Simulated Data (Max., Mean, & Min.)
Substitution of the improved ultimate and reference estimates results in equation (18b) below.
S [lOg(1010
) -lOg(O.25)]-S[lOg(lOS) -lOg(O.2S)]-V[lOg(S x 104
) -log(o.2S)]-U -= . (18b) So log(1010)-log(N) log(lOS)-log(t) log(SXI04)-log(N)
44
The ultimate and reference values in equation (18b) became model parameters or
constraints for the multifactor equation when modified for Inconel718. Figure 30 illustrates
these model parameters graphically, wherein each axis represents an effect.
THERMAL FATIGUE (CYCLES)
N'u 5x10 4
N'o 0.25
No Nu ;--+-----+--1 .. MECHANICAL FATIGUE (CYCLES)
0.25 10 10
CREEP (HOURS)
Fig. 30 Inconel 718 Model Parameters for High-Cycle Mechanical Fatigue, Creep and Thermal Fatigue Effects.
Typical sets of input values for the PRO:MISS model represented by equation (18b)
are given in Tables 13, 14 and 15. For example, Table 13 shows PROMISS input data for a
temperature of 1000 OF, a current value of 2.5xlOS high-cycle mechanical fatigue cycles, a
current value of 1000 creep hours, and a current value of 2000 thermal fatigue cycles. As seen
in Tables 13 through 15, the above-mentioned current values remain the same with the
exception of the current value-ofhigh-cycle mechanical fatigue cycles, N. In Tables 14 and 15
the current value of high-cycle mechanical fatigue cycles has been increased to l.Oxl06 and
1.75xl06, respectively. By holding two of the three sets of current values constant, sensitivity
of lifetime strength towards the third set of values, in this case bigh-cycle mechanical fatigue
cycles, can be ascertained. The complete set of current values that were used as input data for
this sensitivity study are given in Table 16. Notice that the fll"St three rows of the table
correspond to the current values listed in Tables 13, 14 and 15, respectively. The next three
rows of Table 16 show how the current values of creep hours were varied, while the last three
rows show how the current values of thermal fatigue cycles were varied. The results of this
study, in the fonn of cumulative distribution functions, are given in Figures 31 through 33.
45
Figure 31 shows the effect of high-cycle mechanical fatigue cycles on lifetirile strength, while
Figures 32 and 33 show the effect of creep hours and thermal fatigue cycles on lifetime strength, respectively. Note that the c.d.f. shifts to the left, indicating a lowering of lifetime
strength, as mechanical fatigue cycles increase. In this manner, results, in the form of c.d.f.'s,
display the sensitivity of lifetime strength to any current value of an effect
Table 13 '93 Sensitivity Study Input to PROMISS93 for Inconel 718; Temperature = 1000 OF and N=2.5x1OS Cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycles Normal 1.0x1010 1.0x109 10.0 Mechanical N cycles Normal 2.5x1OS 2.5x104 10.0 Fatigue No cycles Normal 0.25 0.025 10.0
s dimensionless Normal 0.2235 0.0067 3.0
Creep tu hours Normal 1.0x1Os 1.0x104 10.0 t hours Normal 1.0x1()3 1.0x102 10.0 to hours Normal 0.25 0.025 10.0 v dimensionless Normal 0.1737 0.0052 3.0
Thermal N'u cycles Normal 5.0x104 5.0x1()3 10.0 Fatigue N' cycles Normal 2.0x1()3 2.0x102 10.0
N'o cycles Normal 0.25 0.025 10.0 u dimensionless Normal 0.191 0.0057 3.0
Table 14 '93 Sensitivity Study Input to PROMISS93 for Ineanel718; Temperature = 1000 OF and N=1.0x106 Cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycles Normal 1.0x1010 1.0x109 10.0 Mechanical N cycles Normal 1.0x106 1.0xlOS 10.0 Fatigue No cycles Normal 0.25 0.025 10.0
s dimensionless Normal 0.2235 0.0067 3.0
Creep tu hours Normal 1.0x1Os 1.0x104 10.0 t hours Normal 1.0x103 1.0x102 10.0 to hours Normal 0.25 0.025 10.0 v dimensionless Normal 0.1737 0.0052 3.0
Thermal N'u cycles Normal 5.0xl04 5.0xl()3 10.0 Fatigue N' cycles Normal 2.0x103 2.0xl02 10.0
N'o cycles Normal 0.25 0.025 10.0 u dimensionless Normal 0.191 0.0057 3.0
46
Table 15 '93 Sensitivity Study Input to PROMISS93 for Inconel 718; Temperature = 1000 of and N=1.75xl06 Cycles
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycles Normal 1.0xl010 1.0x109 10.0 Mechanical N cycles Normal 1.75x106 1.75x1OS 10.0 Fatigue No cycles Normal 0.25 0.025 10.0
s dimensionless Normal 0.2235 0.0067 3.0
Creep tu hours Normal 1.0x1OS 1.0x104 10.0 t hours Normal 1.0x1()3 1.0xl()2 10.0 to hours Normal 0.25 0.025 10.0 v dimensionless Normal 0.1737 0.0052 3.0
Thermal Nu cycles Normal 5.0x104 5.0x1()3 10.0 Fatigue N' cycles Normal 2.0xl()3 2.0x1()2 10.0
No cycles Normal 0.25 0.025 10.0 u dimensionless Normal 0.191 0.0057 3.0
Table 16 Selected Current Values for '93 Sensitivity Study of the Probabilistic Material Strength Degradation Model for Inconel 718.
Fig. 31 Comparison of Various Levels of Uncertainty of High-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel 718 for 2000 Thermal Fatigue
Fig. 35 Comparison of VariOllS Levels of Uncertainty of Low-Cycle Mechanical Fatigue (Cycles) on Probable Strength for 1x106 High-Cycle Mechanical Fatigue Cycles,
2000 Thermal Fatigue Cycles and 1000 Hours of Creep at 1000 of.
Fig. 36 Comparison of Various Levels of Uncertainty of Creep Tune (Hours) on Probable Strength for 1x106 High-Cycle Mechanical Fatigue Cycles, 1000 Low-Cycle Mechanical
Fatigue Cycles and 2000 Thermal Fatigue Cycles at 1000 of.
Fig. 37 Comparison of Various Levels of Uncertainty of Thermal Fatigue (Cycles) on Probable Strength for 1x106 High-Cycle Mechanical Fatigue Cycles, 1000 Low-Cycle Mechanical Fatigue Cycles and 1000 Hours of Creep at 1000 OF.
53
8.0 MODEL VERIFICATION STUDY
Using the probabilistic material strength degradation model embodied in PROMISS,
a model verification study was conducted. The basic assumption, that two or more effects
acting on the material multiply (i.e., independent variables), was evaluated. Available data
allowed for a verification study comparing a combination of high-cycle mechanical fatigue
effects at 75°F and temperature effects at 1000 OF to high-cycle mechanical fatigue effects at
1000 OF. That is, a combination of high-cycle mechanical fatigue and temperature by model
was compared to the combination of these two effects by experiment. The input values for the
combination of these two effects by model are given in Tables 18 through 20, while the input
values for the combination of these two effects by experiment are provided in Tables 21
through 23. Three different current values of high-cycle mechanical fatigue cycles were used
so that the verification study would encompass a range of fatigue cycle values. The results of
this study, in the form of cumulative distribution functions, are given in Figures 38 through 40.
Figure 38 displays lifetime strength predictions for the combination of high-cycle mechanical
fatigue and temperature by model, while Figure 39 displays results for the combination of
these two effects by experiment. Figure 40 is an overlay of the two sets of results. It is
evident that there is approximately a 20% difference between the two sets of distributions.
Due to the questionable high-cycle mechanical fatigue material constant (s = 0.37848)
used in the combination by model input, a second verification study was conducted. Once
again, a combination of these two effects by model was compared to the combination by
experiment. However, an adjusted high-cycle mechanical fatigue material constant (s = 0.141)
was input in place of the questionable high-cycle mechanical fatigue material constant at a
temperature of 75 OF. This value was estimated by noting the percent difference (37 %)
between the calculated slopes at 1000 OF and 1200 OF. The improved input values for this
second verification study are provided in Tables 24 through 26. The input values for
combination by experiment were the same as before. The results are given by Figures 41
through 44. Figure 41, overlays the results for the combination by model and those by
experiment. The 20% difference was greatly reduced. For clarity, Figures 42,43 and 44
overlay the results for both model and experiment for current mechanical fatigue cycle values
of 2.5xl0s, lxl06 and 1.75xl06 cycles, respectively. A percent difference of less than 5%
was observed for all three current mechanical fatigue cycle values.
54
Table 18 Verification Study Input to PROMISS93 for Inconel718; Combination by Model, N=2.5xl()5 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
ffigh-Cycle Nu cycle Normal 1.0xl010 1.0xl09 10.0 Mechanical N cycle Normal 2.5xlOS 2.5xl04 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 75 oF) s dimensionless Normal 0.3785 0.0114 3.0
ffigh Tu OF Normal 2369.0 236.90 10.0 Temperature T OF Normal 1000.0 100.00 10.0 (at lOOO~ To OF Normal 75.0 7.50 10.0
9 dimensionless Normal 0.2422 0.0088 3.6
Table 19 Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=1.0xl06 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
ffigh-Cycle Nu cycle Normal 1.0xl010 1.0x109 10.0 Mechanical N cycle Normal 1.0xl06 1.0xl0s 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 75 oF) s dimensionless Normal 0.3785 0.0114 3.0
High Tu OF Normal 2369.0 236.90 10.0 Temperature T OF Normal 1000.0 100.00 10.0 (at 1000 oF) To OF Normal 75.0 7.50 10.0
q dimensionless Normal 0.2422 0.0088 3.6
Table 20 Verification Study Input to PROMISS93 for Inconel 718; Combination by Model, N=1.75xl06 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
ffigh-Cycle Nu cycle Normal 1.0xl010 1.0xl09 10.0 Mechanical N cycle Normal 1.75 x 106 1.75x1()5 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 75 oF) s dimensionless Normal 0.3785 0.0114 3.0
ffigh Tu OF Normal 2369.0 236.90 10.0 Temperature T OF Normal 1000.0 100.00 10.0 (at 1000 OF) To OF Normal 75.0 7.50 10.0
9 dimensionless Nonnal 0.2422 0.0088 3.6
55
Table 21 Verification Study Input to PROMISS93 for Inconel 718; Combination by Experiment, N=2.5xlOS cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycle Normal 1.0xl010 1.0xl09 10.0 Mechanical N cycle Normal 2.5xlOs 2.5xl04 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 1000 OJ<) s dimensionless Normal 0.2235 0.0067 3.0
Table 22 Verification Study Input to PROMISS93 for Inconel 718; Combination by Experiment, N=1.0xl06 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycle Normal 1.0xl010 1.0xl09 10.0 Mechanical N cycle Normal 1.0xl06 1.0xlOS 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 1000 oF) s dimensionless Normal 0.2235 0.0067 3.0
Table 23 Verification Study Input to PROMISS93 for Inconel718; Combination by Experiment, N=1.75xlQ6 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycle Normal 1.0xl010 1.0xl09 10.0 Mechanical N cycle Normal 1.75xl06 1.75xlOS 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 1000 oF) s dimensionless Normal 0.2235 0.0067 3.0
56
1.0 •
0.8 •
0.6 •
0.4 •
" 1.75x10 6 CYCLES
0.2 o 1.0x10 6 CYCLES
a 2.5x10 5 CYCLES
0.0 • 0.50 0.55 0.60 0.65 0.70 0.75
LIFETIME STRENGTH, SIS 0
Figure 38 Comparison of Various Levels of Uncertainty of High-Cycle Mechanical Fatigue (Cycles) on Probable Strength for Inconel 718.
(Combination ofH-C Mechanical Fatigue and High Temperature Effects by Model)
Figure 40 Overlay of Results for the Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model and Experiment.
58
Table 24 Modified Verification Study Input to PROMISS93 for Inconel718; Combination by Model, N=2.5x1OS cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycle Normal 1.0x1010 l.Ox109 10.0 Mechanical N cycle Normal 2.5x1OS 2.5x104 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 75 oF) s dimensionless Normal 0.141 0.0042 3.0
High Tu OF Normal 2369.0 236.90 10.0 Temperature T OF Normal 1000.0 100.00 10.0 (at 1000 oF) To OF Normal 75.0 7.50 10.0
q dimensionless Normal 0.2422 0.0088 3.6
Table 25 Modified Verification Study Input to PROMISS93 for Inconel718; Combination by Model, N=1.Ox106 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycle Normal 1.0x1010 l.Ox109 10.0 Mechanical N cycle Normal l.Ox106 l.Ox1OS 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 75 OF) s dimensionless Normal 0.141 0.0042 3.0
High Tu OF Normal 2369.0 236.90 10.0 Temperature T OF Normal 1000.0 100.00 10.0 (at 1000 OF) To OF Normal 75.0 7.50 10.0
q dimensionless Normal 0.2422 0.0088 3.6
Table 26 Modified Verification Study Input to PROMISS93 for Inconel718; Combination by Model, N=1.75x106 cycles.
Effect Variable Units Distribution Mean Standard Deviation Symbol Type (Value), (% of Mean)
High-Cycle Nu cycle Normal 1.0x1010 l.Ox109 10.0 Mechanical N cycle Normal 1.75x106 1.75x1OS 10.0 Fatigue No cycle Normal 0.25 0.025 10.0 (at 75 oF) s dimensionless Normal 0.141 0.0042 3.0
High Tu OF Normal 2369.0 236.90 10.0 Temperature T OF Normal 1000.0 100.00 10.0 (at 1000 oF) To OF Normal 75.0 7.50 10.0
dimensionless Normal • 0.2422 0.0088 3.6 9
59
1.0
0.8
0.6
0.4
0.2
0.0
6
0
D
MECH. FATIGUE @ 75 of T @ 1000 of
1.75x10 6 CYCLES
1.0x10 6 CYCLES
2.5x10 5 CYCLES GIltm MECH. FATIGUE 8P.iI @ 1000 of
0.00 0.20 0.40 0.60 0.80 1.00
LIFETIME STRENGTH, SIS 0
Figure 41 Overlay of Results for the Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s) and Experiment.
1.0 -
0.8
0.6 -
0.4
0.2 -C
• 0.0 -
MECH. FATIGUE @ 75 of T @ 1000 of
Combination by Model
Combination by Experiment MECH. FATIGUE @ 1000 of
0.00 0.20 0.40 0.60 0.80 1.00
LIFETIME STRENGTH, SIS 0
Figure 42 Overlay of Results for the Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s)
and Experiment; N=2.SxlOS Cycles.
60
1.0 -
0.8 -
0.6 -
0.4 0
0.2 - • 0.0 -
0.00
MECH. FATIGUE @ 75 of T @ 1000 of
Combination by Model
Combination by Experiment
0.20 0.40 0.60 0.80
LIFETIME STRENGTH, SIS 0
MECH. FATIGUE @ 1000 of
1.00
Figure 43 Overlay of Results for the Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s)
and Experiment; N=1.0xl06 Cycles.
1.0
0.8
0.6
0.4
0.2
0.0
A 6
MECH. FATIGUE @ 75 of T @ 1000 of
Combination by Model
Combination by Experiment MECH. FATIGUE @ 1000 of
0.00 0.20 0.40 0.60 0.80 1.00
LIFETIME STRENGTH, SIS 0
Figure 44 Overlay of Results for the Combination of High-Cycle Mechanical Fatigue and Temperature Effects by Model (Using Estimated Value of s)
and Experiment; N=1.75xl06 Cycles.
61
9.0 DISCUSSION
To ensure model accuracy in lifetime strength predictions, close attention was paid to
model sensitization and calibration. When the current value and the reference value were small
compared to the ultimate value, model transformation, by taking the log of each value within
the product term, was required for model sensitivity. As shown for high-cycle mechanical
fatigue, low-cycle mechanical fatigue, creep and thermal fatigue effects in Figures 5 through 6,
8 through 9, 11 through 12, and 19 through 20, respectively, this transformation resulted in
considerable increases in the linear regression R2 values. The closer the R2 value is to a value
of one, the better the linear regression fit.
Calibration of the model specifically for Inconel 718 required actual experimental
data. Based on this data, initial ultimate and reference values for each effect were estimated and
are provided in Table 9. Linear regression of data individually for each effect resulted in initial
estimates for the empirical material constants. These constants for temperature, high-cycle
mechanical fatigue, low-cycle mechanical fatigue, creep and thermal fatigue effects are given in
Table 10. Further calibration involved adjusting these initial estimates so that y-intercept
(log So) values, resulting from linear regression analysis, corresponded to average yield
strength values of Inconel 718 at specified temperatures. By correlating the So values for all
effects to average yield strengths, accuracy in modeling two or more effects was increased.
These improved estimates are given in Tables 11 and 12. These estimates were used for the
mean values in sensitivity study input files (Tables 13 through 15) to PROMISS93 and
PROMISS94.
Methodology for estimating the variability of the empirical material constants was
developed in Section 6 as a means for dealing with limited data. For the temperature effect, a
standard deviation value of 0.0088 or 3.6% of the mean slope (0.2422) was calculated. This
value, rather than expert opinion, may be used with greater confidence in the probabilistic
material strength degradation model embodied in PROMISS94. Parallel steps may be taken to
determine standard deviation estimates for the empirical material constants of the other effects.
The frrst sensitivity study ('93 Sensitivity Study), discussed in Section 7.0, included
only three effects, high-cycle mechanical fatigue, creep and thermal fatigue, as modeled by
equation (18b). The results of this study, in the form of cumulative distribution functions. are
given in Figures 31 through 33. The sensitivity of lifetime strength to the number of high
cycle mechanical fatigue cycles is seen by the shift of the c.d.f. to the left in Figure 31 as the
number of cycles increases from 2.5x10s to 1.75xl06• The same phenomenon is seen in
Figures 32 and 33. Thus, increasing the current number of the variable decreased the predicted
62
lifetime strength as expected. The temperature effect was not explicitly included in this study
due to the fact that data for the other three effects resulted from tests conducted in a high
temperature environment"(9oo of to 1000 oF). Thus, the effect of temperature is inherent in
the estimated empirical material constants for the other three effects. This is evidenced by the
changing slopes in Figure 23 for the creep effect. The slope or material constant changes
according to the test temperature. At a test temperature of 1000 of, the material constant
(slope) is -0.17372, but increases with temperature to a "steeper" value of -0.75557 at a test
temperature of 1300 of. An increase in the material constant with an increase in temperature is
expected. However, as seen by Figure 21, the high-cycle mechanical fatigue material constant
(slope) is highest at the lowest test temperature of 75 of. Since this slope is based upon only
four questionable data points, it is presumed to be inaccurate. Therefore, based on· observed
trends in the change of slopes for the high-cycle mechanical fatigue effect at temperatures of
1000 OF and 1200 of (Figure 21), an adjusted value for the high-cycle mechanical fatigue
material constant at 75 of was determined. The result was a modified slope 37% less than the
slope obtained at a temperature of 1000 OP. Without additional high-cycle mechanical fatigue
data at a test temperature of 75 OF, this adjusted slope can be neither confirmed nor rejected.
A second sensitivity study C94 Sensitivity Study), discussed in Section 7.0, included
four effects, high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and thermal
fatigue, as modeled by equation (20b). The results of this study, in the form of cumulative
distribution functions, are given in Figures 34 through 37. The sensitivity of lifetime strength
to the number of bigh-cycle mechanical fatigue cycles is seen by the shift of the c.df. to the left
in Figure 34 as the number of cycles increases from 2.5x10s to 1.75x106• The same
phenomenon is seen in Figures 35 through 37. Thus, increasing the current number of the
variable decreased the predicted lifetime strength as expected. As with the '93 Sensitivity
Study, the temperature effect was not explicitly included in the '94 Sensitivity Study since it is
inherent in the estimated empirical material constants for the other four effects. Comparison of
results between the '94 Sensitivity Study and the '93 Sensitivity Study, show a reduction in
Lifetime Strength, S/So. This was expected since each effect contributes to the decrease in the
lifetime strength of the material. Thus, lifetime strength values resulting from a study
including four effects will be lower than values resulting from a study including only three
effects.
Both the questionable (s = 0.37848) and the adjusted (s = 0.141) high-cycle
mechanical fatigue material constants at 75 OP were used in verification studies presented in
Section 8. Available data allowed for a verification study comparing a combination of high
cycle mechanical fatigue and temperature effects by model to the combination of these two
effects by experiment. The results of this study, in the form of c.dJ.'s, are given in Figures 38
63
through 40. The sensitivity of lifetime strength to the number of current mechanical fatigue
cycles is seen by the shift of the c.d.f. to the left (Figures 38 and 39) as the number of cycles
increases. Thus, increasing the number of current fatigue cycles decreases the predicted
lifetime strength as expected. As seen by the overlay of distributions in Figure 40, there is
approximately a 20% difference between the results obtained by model and those obtained by
experiment. A major possibility for this large discrepancy is the questionable high-cycle
mechanical fatigue material constant at 75 OF. To test this assumption, a second parallel
verification study using the adjusted high~cycle mechanical fatigue material constant value was
conducted. The results are given in Figures 41 through 44. Comparison of Figure 41 to
Figure 40 shows a substantial decrease in the discrepancy between the two sets of
distributions. From Figures 42 through 44, it is apparent that the percent difference between
the results is less than 5% for all three current values of fatigue cycles evaluated. Thus, the
questionable high-cycle mechanical fatigue material constant calculated from the high-cycle
mechanical fatigue data at 75 OP was responsible for a large percent of the discrepancy between
the initial results from the fIrst verification study.
64
10.0 CONCLUSIONS
A probabilistic material strength degradation model, applicable to aerospace
materials, has been postulated for predicting the random lifetime strength of structural
components for propulsion system components sUbjected to a number of effects. This model,
in the form of a randomized multifactor equation, has been developed for five effects, namely,
high temperature, high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and
thermal fatigue. Inconel 718 data for these effects was obtained from the open literature.
Based on this data, initial ultimate and reference values were estimated. It was determined that
when the current and reference values are small compared to the ultimate value the model is
insensitive. Therefore, a transformation to sensitize the model for the effects of high-cycle and
low-cycle mechanical fatigue, creep and thermal fatigue was required. Model transformation
resulted in significant increases in the R2 (goodness of fit) values. The current version of
PROMISS,entitIed PROMISS94, provides for this transformation for these four effects.
Linear regression of the data for each effect resulted in, estimates for the empirical
material constants, as given by the slope of the linear fit. These estimates, together with
ultimate and reference values, were used to calibrate the model specifically for Inconel 718. By
adjusting these initial estimates so that the y-intercept or So values corresponded to average
yield strength values of Inconel 718, accuracy in modeling two or more effects was improved.
Thus, model accuracy is dependent on the proper selection of ultimate and reference values,
which in tum influence the values of the empirical material constants used in calibration of the
model. Calibration of the model for other materials is also dependent on experimental data and
is not possible without it.
Methodology for estimating the standard deviation of empirical material constants
offered a way for dealing with limited data. This methodology results in better estimates of the
standard deviations based on actual experimental data, rather than expert opinion. Lack. of
sufficient data from which to evaluate the material constants warranted the development of this
methodology.
Results from two separate sensitivity studies involving three and four effects,
respectively, showed that the c.d.f.'s shift to the left, indicating a lowering of lifetime strength,
for increasing current values of an effect. As expected, comparison between the '94 Sensitivity
Study and the '93 Sensitivity Study revealed a reduction in the lifetime strength values. Thus,
the more effects included in a study, the lower the resulting lifetime strength values. Further
development and evaluation of the three and four effect models, as well as other models,
requires that they be compared to real responses of Inconel 718 samples subjected to the same
65
combined effects during experimentation. Thus, additional experimental data is crucial for the
continued development and evaluation of the probabilistic material strength degradation model
presented in this report.
Limited verification studies involving two effects, high-cycle mechanical fatigue and
high temperature, were conducted. Results showed a combination of the two effects by model
to be more conservative than the combination by experiment. The fJIst verification study
yielded a 20% discrepancy between the results obtained by model and those obtained by
experiment. Questionable high-cycle mechanical fatigue data at a temperature of 75 OP is
presumed to be a major cause of the discrepancy. This conclusion was drawn after conducting
a second verification study using an adjusted value in place of the questionable one. The
outcome was a significant reduction in the discrepancy, from 20% to less than 5%, between the
results of a combination of these two effects by model and the combination by experiment.
Therefore, the data, rather than the nature of the model, is the presumed source of error. Thus,
the basic assumption of the model, that two or more effects multiply (Le., effects are
independent), is strongly supported by this limited verification study. The remaining 5%
difference may be due to the lack of uniformity among the specimens tested. As seen by Table
A.5 in the Appendix, specimen shape and heat treatment varied between the effects. Specimen
shape, as well as heat treatment, can influence material properties. Another reason for the 5%
difference may be synergistic effects (i.e., dependence between effects). As previously
discussed, equation (1) is an approximated solution to a separable partial differential equation.
In order to account for synergistic effects and perhaps eliminate this 5% difference, additional
terms would have to be added to equation (1). The resulting reduction in error mayor may not
warrant complication of the model by the inclusion of additional terms. Based on the results
obtained from the second verification study, this complication is not warranted. However,
additional verification studies for the combination of other effects must fJISt be conducted
before a more refined model can be developed. As previously discussed, the availability of
experimental data will determine whether or not further studies can be conducted.
In conclusion, methodology for improving lifetime strength prediction capabilities is
presented. The probabilistic material strength degradation model in the form of a randomized
multifactor equation is developed for five effects and calibrated to best reflect physical reality
for Inconel 718. Systematic and repeatable methods of model calibration and evaluation are
developed. Basic understanding and evaluation of the model is generated through sensitivity
and verification studies. The sensitivity of random lifetime strength to any current value of an
effect can be ascertained. Probability statements in the form of cumulative distribution
functions allow improved judgments to be made regarding the likelihood of lifetime strength,
thus enabling better design decisions to be made.
66
I
"
·11.0 ACKNOWLEDGMENTS
The authors gratefully acknowledge the many helpful conversations with
Dr. Christos C. Chamis and the support of NASA Lewis Research Center.
67
12.0 APPENDIX
This appendix provides the experimental Inconel718 data analyzed by the postulated material strength degradation model. The purpose of this appendix is to allow the calculations of Section S to be repeated. Data for all effects will be presented in tabular form. Tables A.1-
A.S present the high temperature, high-cycle mechanical fatigue, low-cycle mechanical fatigue,
thermal fatigue and creep data, respectively. Table A.6 provides reference numbers and figure
numbers for displayed data, as well as, specimen and heat treatment specifications for all data
presented in this report.
Table A.1 Inconel 718 High Temperature Tensile Data.
16 Korth, G. E., "Mechanical Properties Test Data of Alloy 718 for Liquid Metal Fast Breeder Reactor Applications," EG&G Report No. EGG-2229, January, 1983.
17 Kuwabara, K., Nitta, A. and Kitamura, T., "Thermal-Mechanical Fatigue Life Prediction in High-Temperature Component Materials for Power Plant," Proceedings of the
Advances in Life Prediction Methods Conference, AS ME, Albany, N. Y., April, 1983,
pp. 131-141.
18 Mendenhall, W., Introduction to Probability and Statistics, Duxbury Press, North
Scituate, Massachusetts, 1979, p. 48.
19 Ross, S. M., Introduction to Probability and Statistics for Engineers and Scientists,
Wiley, New York, 1987, p. 278.
73
REFERENCES (continued)
20 Scott, D. W~, "Nonparametric Probability Density Estimation by Optimization Theoretic Techniques," NASA CR-147763, April 1976.
21 Shigley, J. E. and Mischke C. R., Mechanical Engineering Design, 5th Ed., McGraw
Hill, N. Y., 1989, p. 161.
22 Siddall, J. N., Probabilistic Engineering Design, Marcel Dekker, Inc., New York, 1983.
23 Sims, C. T., Stoloff, N.S. and Hagel, W.C., Superalloys II, Wiley, New York, 1987,
pp. 581-585, 590-595.
24 Swindeman, R. W. and Douglas, D.A., "The Failure of Structural Metals Subjected to Strain-Cycling Conditions," Journal of Basic Engineering, ASME Transactions, 81, Series D, 1959, pp. 203 -212.
74
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Probabilistic Material Strength Degradation Model for Inconel718 Components Subjected to High Temperature, High-Cycle and Low-Cycle Mechanical Fatigue, Creep and Thermal Fatigue Effects WU-505-62-10
6. AUTHOR(S) G-NAG3-867
Callie C. Bast and Lola Boyce
7. PERFORMING ORGANIZAnON NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER
The University of Texas at San Antonio The Division of Engineering E-lOO12 San Antonio, Texas 78249
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National Aeronautics and Space Administration Lewis Research Center NASA CR-198426 Cleveland, Ohio 44135-3191
11. SUPPLEMENTARY NOTES
Project Manager, C.C. Chamis, Structures Division, NASA Lewis Research Center, organization code 5200, (216) 433-3252.
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13. ABSTRACT (Maximum 200 words)
The development of methodology for a probabilistic material strength degradation is described. The probabilistic model, in the form of a postulated randomized multifactor equation, provides for quantification of uncertainty in the lifetime material strength of aerospace propulsion system components subjected to a number of diverse random effects. This model is embodied in the computer program entitled PROMISS, which can include up to eighteen different effects. Presently, the model includes five effects that typically reduce lifetime strength: high temperature, high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and thermal fatigue. Results, in the form of cumulative distribution functions, illustrated the sensitivity of lifetime strength to any current value of an effect. In addition, verification studies comparing predictions of high-cycle mechanical fatigue and high temperature effects with experiments are presented. Results from this limited verification study strongly supported that material degradation can be represented by randomized multifactor interaction models.
14. SUBJECT TERMS
Uncertainties; Material degradation; Computer programs; Data; Regression parameters; Calibration; Linear regression distributions; Comparisons
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